The design of 3D constructs with adequate properties to instruct and guide cells both in vitro and in vivo is one of the major focuses of tissue engineering. Successful tissue regeneration depends on the favorable crosstalk between the supporting structure, the cells and the host tissue so that a balanced matrix production and degradation are achieved. Herein, the major occurring events and players in normal and regenerative tissue are overviewed. These have been inspiring the selection or synthesis of instructive cues to include into the 3D constructs. We further highlight the importance of a multiscale perception of the range of features that can be included on the biomimetic structures. Lastly, we focus on the current and developing tissue-engineering approaches for the preparation of such 3D constructs: top-down, bottom-up and integrative. Bottom-up and integrative approaches present a higher potential for the design of tissue engineering devices with multiscale features and higher biochemical control than top-down strategies, and are the main focus of this review.